BPS Action and Superpotential for Heterotic String Compactifications with Fluxes

We consider = 1 compactifications to four dimensions of heterotic string theory in the presence of fluxes. We show that up to order (α'2) the associated action can be written as a sum of squares of BPS-like quantities. In this way we prove that the equations of motion are solved by backgrounds which fulfill the supersymmetry conditions and the Bianchi identities. We also argue for the expression of the related superpotential and discuss the radial modulus stabilization for a class of examples.